1. 9.5 – Adding and Subtracting Rational Expressions

2. In order to add or subtract fractions we need a common denominator We want the Lowest Common Denominator (LCD) before we add or subtract LCD: 15LCD: 36

3. ADDING and SUBTRACTING RATIONALS - Finding LCM 10x², 35x²  _______________________ 4x³, 5x²y  _______________________ x-y, x²-y²  _______________________ x²-5x+4, x – 2  ___________________ 70x² 20x³y (x-y)(x+y) (x-4)(x-1)(x-2)

4. ADDING and SUBTRACTING Adding ADD/SUBTRACT Rules 1)Factor denominators 2)Find LCM 3)Multiply each term to get denominator = LCM 4)+/- and combine like terms 5)Simplify more if possible

5. ADDING and SUBTRACTING Subtracting Factor denominators Multiply terms to get LCMs on bottom Simplify Combine like termsFactor top Simplify

6. ADDING and SUBTRACTING A Toughie FACTOR FACTOR -OUT CONVERT SIMPLIFY COMBINE SIMPLIFY

7. Let’s try one

11. COMPLEX FRACTIONS What are complex fractions? Complex fractions are giant expressions where there are fractions within fractions. The goal is to simplify them down to normal fractions.

12. EX – simplify SIMPLIFYING COMPLEX FRACTIONS STEPS 1)Find LCM of denoms 2)Treat each fraction as an individual problem. Find the LCM and add or subtract. 3)Divide the rational expressions. 4)Simplify

13. EX - simplify FACTOR OUT -1 MULT TOP/BOT by LCM DISTRIBUTE LCM SIMPLIFY DIVIDE THE RATIONALS

14. Let’s try one